Morava $E$-theory source of reading

Question

Recently I came across a paper which I really need to read through and which uses language of Morava $E$-theory. Since I'm not comfortable with this cohomology theory, I've been looking for quite a while some source to read (at least the basics) but wasn't able to find out something concrete. Does anyone know where can someone learn about Morava $E$-theory? I highly doubt that some self-contained textbook exists that covers this particular material, therefore any instructive paper or preprint is what am looking for most likely!

P.S. The same question had been asked yesterday on MSE, where I got no answer or comment (I deleted today). I didn't know if it is or not suitable for MSE from the beginning, therefore I ask here!

I don't know what your background in homotopy theory is, but Lurie's notes at http://www.math.harvard.edu/~lurie/252x.html and Rezk's paper http://www.math.uiuc.edu/~rezk/hopkins-miller-thm.pdf are very nice. — skd, Jun 11 '18 at 15:37
@skd That should be an answer. Also, let me mention Ravenel's Nilpotence and periodicity — Denis Nardin, Jun 11 '18 at 15:39
@skd Indeed that could be an answer, at Lecture 21 Lurie defines it, and seems that sets up the background to do so nicely in the previous lectures. Thank you! — mayer_vietoris, Jun 11 '18 at 15:46

score 4 · Answer 1 · answered Jun 11 '18 at 22:02

Lurie's notes at http://www.math.harvard.edu/~lurie/252x.html and Rezk's notes http://www.math.uiuc.edu/~rezk/hopkins-miller-thm.pdf explicitly discuss Morava E-theory.
Eric Peterson's book project at https://github.com/ecpeterson/FormalGeomNotes also discusses Morava E-theory in detail in sections 3.4 and onwards.
As Denis mentions in the comments, Ravenel's "orange book" (available at https://web.math.rochester.edu/people/faculty/doug/mybooks/nilpb.pdf) is also a good resource to learn chromatic homotopy theory from, although Morava E-theory is not explicitly discussed there.
Yet another source is the latter few sections of the famous COCTALOS notes at http://web.math.rochester.edu/people/faculty/doug/otherpapers/coctalos.pdf, but they're not edited, and hence lack a lot of details.
Finally, I'd previously written an answer on MathOverflow, at Has anyone seen a nice map of multiplicative cohomology theories?, giving a disappointingly brief overview of chromatic homotopy theory. There are better sources to read from, but I've linked to some references in that answer.

Morava $E$-theory source of reading

1 Answers1